Evolution of the fire‐hose instability: Linear theory and wave‐wave coupling

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Abstract
Large ion thermal or kinetic pressure anisotropies have been inferred to exist in conjunction with supernova shocks as well as in the solar wind/cometary interaction region and upstream from planetary bow shocks. For sufficiently strong thermal or beam‐driven anisotropies, electromagnetic instability develops, isotropizing and scattering the ion populations. In particular, if the effective plasma β > 2 (where β is the ratio of plasma pressure to magnetic pressure), and if the anisotropy is such that the temperature parallel to the magnetic field exceeds the perpendicular, then fire‐hose instability can result, generating transverse magnetic field fluctuations. In high‐β interstellar plasmas with large anisotropies, the level of the excited fluctuations may be quite large, exceeding even the ambient magnetic field. After a period of inverse‐cascade to longer wavelengths, it may provide a potential source for the scattering of cosmic rays. In this study we simulate the evolution of the fire‐hose instability using a standard one‐dimensional hybrid code (macroparticle ions, massless fluid electrons). We find that the wave evolution proceeds in two stages. A rapid period of growth brings the plasma back to approximate marginal stability. There follows a second stage of slower evolution dominated by wave‐wave interaction. During the second stage, the wave energy spectrum clearly exhibits an inverse cascade. Implications for cosmic ray scattering will be discussed.